Multiple Time Windows for Technician Routing

Answered

Baris Kafa

March 07, 2024 07:45

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Hello, 

I want to add multiple time windows for Techician Routing Scheduling Examples in Gurobi Example. 

How can i do that? Could you share some code blocks? 

Thank you. 

 

Related to

• Scheduling

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  Riley Clement

  • Gurobi Staff

  March 08, 2024 10:08

  Hi Baris,

  Is the problem you're considering an extension of the one in this notebook:
  https://colab.research.google.com/github/Gurobi/modeling-examples/blob/master/technician_routing_scheduling/technician_routing_scheduling.ipynb
  but where each customer has a set of disjoint time windows that the technician can arrive in, instead of a single time window?

  - Riley

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  Baris Kafa

  March 11, 2024 07:08 Edited

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  Hi Riley, 

  i see that notebook. My question is about a customer having multiple time windows.

  This is how we currently use it.
  tStart = {j.name : j.tStart for j in customers}
  tEnd = {j.name : j.tEnd for j in customers}

  The form I want to use is;
  tStart1 = {j.name : j.tStart1 for j in customers}
  tEnd1 = {j.name : j.tEnd1 for j in customers}

  tStart2 = {j.name : j.tStart2 for j in customers}
  tEnd2 = {j.name : j.tEnd2 for j in customers}

  tStart3 = {j.name : j.tStart3 for j in customers}
  tEnd3 = {j.name : j.tEnd3 for j in customers}

  
  How can I combine these 3 different time windows?

  Thank you. 

  -Baris

   

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  Riley Clement

  • Gurobi Staff

  March 11, 2024 09:54

  Hi Baris,

  Currently the time windows are enforced with the following constraints,

  t_j >= a_j - xa_j
  t_j <= b_j + xb_j

  where t_j is the arrival time at location j, and time window at location j is [a_j, b_j].

  Suppose instead you want 3 time windows, [a_{j1}, b_{j1}], [a_{j2}, b_{j2}], [a_{j3}, b_{j3}].  You can introduce binary variables w_{j1}, w_{j2}, w_{j3} to indicate the choice of window.  You have to introduce constraints for each j to make sure a window is chosen:

  w_{j1} + w_{j2} + w_{j3} = 1

  and then the start time of the window is equal to

  a_{j1}w_{j1} + a_{j2}w_{j2} + a_{j3}w_{j3}

  and the end time of the window is equal to

  b_{j1}w_{j1} + b_{j2}w_{j2} + b_{j3}w_{j3}

  and you can use these expressions in place of a_j and b_j in the original time window constraints.

  - Riley

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